A structure including a support defining an opening, and a tensilely stressed thin-film membrane disposed to occlude the opening, the membrane contacting at least a portion of the support. The stressed membrane includes a material having a characteristic crack spacing greater than one-half of a minimum dimension of the membrane and less than ten times the minimum dimension. A structure including a support defining a opening having a minimum opening dimension, and a compressively stressed thin-film membrane disposed to occlude the opening, the membrane contacting at least a portion of the support. The stressed membrane includes a membrane material having a critical aspect ratio for buckling that is greater than a ratio of one-half of the minimum opening dimension to a thickness of the membrane, and the critical aspect ratio for buckling is less than a ratio of ten times the minimum opening dimension to the thickness of the membrane.